a tetrahedral site
A tetrahedral site is the smaller of the two interstitial holes in a close-packed crystal. Picture three touching spheres in one layer with a fourth sphere resting in the dimple on top: the little cavity at the centre, surrounded by four spheres whose centres form a tetrahedron, is the tetrahedral site. Any atom that sits there has coordination number 4.
Because it is boxed in by only four neighbours, it is a tight fit. Geometry says a sphere just filling a tetrahedral hole without pushing the host apart has a radius ratio of about 0.225, and the hole can accept guests up to a radius ratio of about 0.414 before it is more comfortable in the larger octahedral hole. In the FCC cell there are 8 tetrahedral sites, located at the eight (1/4, 1/4, 1/4)-type positions inside the cube, twice as many as the octahedral sites.
Tetrahedral occupancy builds some of the most important compound structures. Zinc blende is an FCC array of sulfur with zinc filling half of the tetrahedral holes; wurtzite is the HCP version of the same idea; and in spinel the smaller A cations sit on tetrahedral sites. Whenever you see fourfold coordination in an oxide or semiconductor, tetrahedral interstitials are usually the reason.
In zinc blende, zinc occupies exactly half of the eight tetrahedral holes of the FCC sulfur array, giving each ion coordination 4.
Four-around-one: the tetrahedral hole is the tight one, twice as numerous as the octahedral.
There are twice as many tetrahedral holes as octahedral holes in close packing (8 versus 4 per FCC cell), but they are smaller, so only sufficiently tiny cations use them.